That starter clutch thing is weird Seth, I've had over 20 CB750's over the past 36 years and I've not had a problem with the actual gears. I did have a bad starter motor that made some horrible noises when I was riding the bike, while barely able to turn over my stock F2 engine, but nothing like you've described?
I hate Valvoline oil in bikes. I had all the same problems you've described the one time that I used it in my Z1, the clutch was either "on" or "off", with nothing in between, I either had to rev it up and wheelie away, or stall it, and there was no way I could find neutral. I dumped that crap out and refilled it with some cheaper Mobil oil, and never had that problem again.
Change your oil Seth, and I bet the problem goes away. Cheers, Terry.